Exploration of Stable Atomic Configurations in Graphene-like BCN Systems by Density Functional Theory and Bayesian Optimization

h-BCN is an intriguing material system where the bandgap varies considerably depending on the atomic configuration, even at a fixed composition. Exploring stable atomic configurations in this system is crucial for discussing the energetic formability and controllability of desirable configurations. In this study, this challenge is tackled by combining first-principles calculations with Bayesian optimization. An encoding method that represents the configurations as vectors, while incorporating information about the local atomic environments and domain knowledge, is proposed for the search. The proposed encoding method proved effective in the search, resulting in the discovery of two interesting and stable semiconductor configurations (zigzag-type and armchair-type stripe configurations). Furthermore, the optimization behavior is discussed through principal component analysis, confirming that the ordered BN network and the C configuration features are well embedded in the search space. While previous studies have investigated a limited number of empirically prepared h-BCN configurations, this study enables the efficient exploration of stable configurations from a vast number of candidates. Our approach is expected to be systematically applicable to various compositions and periodicities, contributing to the design of atomic configurations for semiconductor device applications of h-BCN.